Question

A pendulum has period T for small oscillations.An obstacle is placed directly beneath the pivot, so that only the lowest one quarter of the string can follow the pendulum bob when it swings to the left of its resting position as shown in the figure. The pendulum is released from rest at a certain point A. The time taken by it to return to that point is nT/4. Find the value of n ?

Answer 1

T ∝ √length free length becomes l/4 So time period becomes T₁ = T/2

Half oscillation is with free length l and half with free length l/4

Total time = T/2 + T₁/2 = 3T/4